Giffords' husband, Mark Kelly, is excited by the progress in her attention span

Neurosurgeon says she's showing improvements every day

Houston (CNN) -- U.S. Rep. Gabrielle Giffords was making "lightning speed" progress for a brain injury and had the drain for brain fluid removed from her head, her doctors said Wednesday.

"Since Gabby arrived last Friday, we noticed daily improvement in her neurological condition," Dr. Dong Kim, chairman of neurosurgery at the University of Texas Medical School, said during Wednesday's media briefing. "In terms of recovering from brain issues, this is really at lightning speed."

Giffords is still unable to speak, and she's unable to sit or stand on her own, doctors said. The Arizona Democrat, who survived an assassination attempt, was moved from a Houston hospital to a nearby rehabilitation hospital on Wednesday after doctors upgraded her condition to good from serious.

Giffords is now receiving therapies in The Institute for Rehabilitation and Research Memorial Hermann, also known as TIRR Memorial Hermann, according to Rebecca Moran, spokeswoman for Memorial Hermann.

"She is undertaking the physical therapy and occupational therapy and speech therapy this afternoon," Kim said at the briefing.

Meanwhile, Jared Lee Loughner, who allegedly tried to assassinate Giffords, had spent time searching the internet and was curious about others who had pulled off political assassinations, a law enforcement source told CNN.

The story was first reported in The Washington Post online Wednesday.

Loughner spent time on the internet as he was allegedly getting ready to carry out a gun attack on Giffords, and Loughner's personal computer, seized by authorities following the attack, indicates he was surfing various websites about political killers, the source told CNN.

The law enforcement source declined to identify whom Loughner had researched. The source requested anonymity because of the ongoing criminal investigation.

Loughner also looked at information about lethal injections and solitary confinement, according to the source. He visited the websites in the weeks and even days leading up to the shooting, the source added.

Thirty-two shots were fired in the January 8 rampage that killed six people -- including a chief federal judge, a 9-year old girl and two congressional aides -- and wounded 13 more peopel, including Giffords, who was shot in the head at an outdoor "meet and greet" with constituents.

Loughner is charged with trying to kill Giffords and two of her aides, Ron Barber and Pamela Simon. Federal prosecutors have indicated more charges are forthcoming.

In Houston, Giffords' upgraded condition was announced late Tuesday after her husband, Mark Kelly, said she had watched an hour of television from her hospital bed.

Kelly called the development "exciting," said Rep. Debbie Wasserman Schultz, D-Florida and a friend of Giffords.

"Last night or the night before she watched television -- it was CNN in fact --- and the fact that she was able to do that for about an hour, in terms of attention span, they were pretty excited about that," Wasserman Schultz said.

Kelly remains optimistic that his wife will make a full recovery, she said.

"Doctors continue to tell them they're hopeful about how much she'll recover. With each day, she's able to do things that are a little more complex than she had been doing before," she said.

A federal judge entered a plea of not guilty Monday on behalf of Jared Lee Loughner to three counts of attempted murder in the mass shooting that wounded U.S. Rep. Gabrielle Giffords earlier this month.